(7x-x^2)/(x^2-8x+7)-(4x^2+4x+1)/(1-4x^2)

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(7x-x^2)/(x^2-8x+7)-(4x^2+4x+1)/(1-4x^2)

(7x-x^2)/(x^2-8x+7)-(4x^2+4x+1)/(1-4x^2)
(7x-x^2)/(x^2-8x+7)-(4x^2+4x+1)/(1-4x^2)

(7x-x^2)/(x^2-8x+7)-(4x^2+4x+1)/(1-4x^2)
(7x-x^2)/(x^2-8x+7)-(4x^2+4x+1)/(1-4x^2)
=-x(x-7)/(x-7)(x-1)-(2x+1)^2/(1-2x)(1+2x)
=-x/(x-1)-(2x+1)/(1-2x)
=-x/(x-1)+(2x+1)/(2x-1)
=[-x(2x-1)+(x-1)(2x+1)]/(2x-1)(x-1)
=[-2x^2+x+2x^2+x-2x-1]/(2x-1)(x-1)
=-1/(2x-1)(x-1)

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